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Basic Technical Mathematics with Calculus,9780321131942
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Basic Technical Mathematics with Calculus

by
Edition:
9th
ISBN13:

9780321131942

ISBN10:
0321131940
Format:
Hardcover
Pub. Date:
1/1/2009
Publisher(s):
Prentice Hall

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Summary

This tried-and-true text from the pioneer of the basic technical mathematics course now has Addison-Wesley's amazing math technologies MyMathLab and MathXL helping students to develop and maintain the math skills they will need in their technical careers.Technical mathematics is a course pioneered by Allyn Washington, and the eighth edition of this text preserves the author's highly regarded approach to technical math, while enhancing the integration of technology in the text. The book is intended for a two- or three-semester course and is taught primarily to students who plan to pursue technical fields. The primary strength of the text is the heavy integration of technical applications, which aids the student in pursuit of a technical career by showing the importance of a strong foundation in algebraic and trigonometric math.Allyn Washington defined the technical math market when he wrote the first edition of Basic Technical Mathematics over forty years ago. His continued vision is to provide highly accurate mathematical concepts based on technical applications. The course is designed to allow the student to be simultaneously enrolled in allied technical areas, such as physics or electronics. The material in the text can be easily rearranged to fit the needs of both instructor and students. Above all, the author's vision of this book is to continue to enlighten today's students that an understanding of elementary math is critical in many aspects of life.

Table of Contents

Basic Algebraic Operations
1(49)
Numbers
2(4)
Fundamental Operations of Algebra
6(5)
Calculators and Approximate Numbers
11(5)
Exponents
16(5)
Scientific Notation
21(3)
Roots and Radicals
24(2)
Addition and Subtraction of Algebraic Expressions
26(4)
Multiplication of Algebraic Expressions
30(2)
Division of Algebraic Expressions
32(4)
Solving Equations
36(3)
Formulas and Literal Equations
39(3)
Applied Word Problems
42(8)
Chapter Equations, Review Exercises, and Practice Test
46(4)
Geometry
50(31)
Lines and Angles
51(3)
Triangles
54(7)
Quadrilaterals
61(3)
Circles
64(4)
Measurement of Irregular Areas
68(4)
Solid Geometric Figures
72(9)
Chapter Equations, Review Exercises, and Practice Test
76(5)
Functions and Graphs
81(29)
Introduction to Functions
82(3)
More about Functions
85(5)
Rectangular Coordinates
90(2)
The Graph of a Function
92(6)
Graphs on the Graphing Calculator
98(5)
Graphs of Functions Defined by Tables of Data
103(7)
Review Exercises and Practice Test
107(3)
The Trigonometric Functions
110(27)
Angles
111(3)
Defining the Trigonometric Functions
114(4)
Values of the Trigonometric Functions
118(4)
The Right Triangle
122(5)
Applications of Right Triangles
127(10)
Chapter Equations, Review Exercises, and Practice Test
132(5)
Systems of Linear Equations; Determinants
137(39)
Linear Equations
138(3)
Graphs of Linear Functions
141(4)
Solving Systems of Two Linear Equations in Two Unknowns Graphically
145(4)
Solving Systems of Two Linear Equations in Two Unknowns Algebraically
149(7)
Solving Systems of Two Linear Equations in Two Unknowns by Determinants
156(5)
Solving Systems of Three Linear Equations in Three Unknowns Algebraically
161(5)
Solving Systems of Three Linear Equations in Three Unknowns by Determinants
166(10)
Chapter Equations, Review Exercises, and Practice Test
171(5)
Factoring and Fractions
176(40)
Special Products
177(3)
Factoring: Common Factor and Difference of Squares
180(5)
Factoring Trinomials
185(6)
The Sum and Differences of Cubes
191(2)
Equivalent Fractions
193(5)
Multiplication and Division of Fractions
198(4)
Addition and Subtraction of Fractions
202(6)
Equations Involving Fractions
208(8)
Chapter Equations, Review Exercises, and Practice Test
212(4)
Quadratic Equations
216(19)
Quadratic Equations; Solution by Factoring
217(4)
Completing the Square
221(3)
The Quadratic Formula
224(4)
The Graph of the Quadratic Function
228(7)
Chapter Equations, Review Exercises, and Practice Test
232(3)
Trigonometric Functions of Any Angle
235(23)
Signs of the Trigonometric Functions
236(2)
Trigonometric Functions of Any Angle
238(6)
Radians
244(5)
Applications of Radian Measure
249(9)
Chapter Equations, Review Exercises, and Practice Test
254(4)
Vectors and Oblique Triangles
258(34)
Introduction to Vectors
259(4)
Components of Vectors
263(4)
Vector Addition by Components
267(5)
Applications of Vectors
272(5)
Oblique Triangles, the Law of Sines
277(7)
The Law of Cosines
284(8)
Chapter Equations, Review Exercises, and Practice Test
289(3)
Graphs of the Trigonometric Functions
292(25)
Graphs of y = a sin x and y = a cos x
293(3)
Graphs of y = a sin bx and y = a cos bx
296(4)
Graphs of y = a sin(bx + c) and y = a cos(bx + c)
300(3)
Graphs of y = tan x, y = cot x, y = sec x, y = csc x
303(3)
Applications of the Trigonometric Graphs
306(3)
Composite Trigonometric Curves
309(8)
Chapter Equations, Review Exercises, and Practice Test
313(4)
Exponents and Radicals
317(22)
Simplifying Expressions with Integral Exponents
318(4)
Fractional Exponents
322(5)
Simplest Radical Form
327(3)
Addition and Subtraction of Radicals
330(3)
Multiplication and Division of Radicals
333(6)
Chapter Equations, Review Exercises, and Practice Test
337(2)
Complex Numbers
339(31)
Basic Definitions
340(3)
Basic Operations with Complex Numbers
343(3)
Graphical Representation of Complex Numbers
346(3)
Polar Form of a Complex Number
349(3)
Exponential Form of a Complex Number
352(3)
Products, Quotients, Powers, and Roots of Complex Numbers
355(6)
An Application to Alternating-Current (ac) Circuits
361(9)
Chapter Equations, Review Exercises, and Practice Test
367(3)
Exponential and Logarithmic Functions
370(29)
Exponential Functions
371(2)
Logarithmic Functions
373(4)
Properties of Logarithms
377(5)
Logarithms to the Base 10
382(3)
Natural Logarithms
385(3)
Exponential and Logarithmic Equations
388(4)
Graphs on Logarithmic and Semilogarithmic Paper
392(7)
Chapter Equations, Review Exercises, and Practice Test
396(3)
Additional Types of Equations and Systems of Equations
399(17)
Graphical Solution of Systems of Equations
400(3)
Algebraic Solution of Systems of Equations
403(4)
Equations in Quadratic Form
407(3)
Equations with Radicals
410(6)
Review Exercises and Practice Test
414(2)
Equations of Higher Degree
416(19)
The Remainder and Factor Theorems; Synthetic Division
417(5)
The Roots of an Equation
422(5)
Rational and Irrational Roots
427(8)
Chapter Equations, Review Exercises, and Practice Test
433(2)
Matrices
435(23)
Definitions and Basic Operations
436(4)
Multiplication of Matrices
440(5)
Finding the Inverse of a Matrix
445(5)
Matrices and Linear Equations
450(8)
Chapter Equations, Review Exercises, and Practice Test
454(4)
Inequalities
458(30)
Properties of Inequalities
459(4)
Solving Linear Inequalities
463(5)
Solving Nonlinear Inequalities
468(7)
Inequalities Involving Absolute Values
475(3)
Graphical Solution of Inequalities with Two Variables
478(3)
Linear Programming
481(7)
Chapter Equations, Review Exercises, and Practice Test
485(3)
Variation
488(15)
Ratio and Proportion
489(4)
Variation
493(10)
Chapter Equations, Review Exercises, and Practice Test
499(4)
Sequences and the Binomial Theorem
503(21)
Arithmetic Sequences
504(5)
Geometric Sequences
509(4)
Infinite Geometric Series
513(3)
The Binomial Theorem
516(8)
Chapter Equations, Review Exercises, and Practice Test
521(3)
Additional Topics in Trigonometry
524(35)
Fundamental Trigonometric Identities
525(7)
The Sum and Difference Formulas
532(5)
Double-Angle Formulas
537(4)
Half-Angle Formulas
541(3)
Solving Trigonometric Equations
544(5)
The Inverse Trigonometric Functions
549(10)
Chapter Equations, Review Exercises, and Practice Test
555(4)
Plane Analytic Geometry
559(49)
Basic Definitions
560(4)
The Straight Line
564(6)
The Circle
570(4)
The Parabola
574(5)
The Ellipse
579(5)
The Hyperbola
584(6)
Translation of Axes
590(3)
The Second-Degree Equation
593(3)
Polar Coordinates
596(4)
Curves in Polar Coordinates
600(8)
Chapter Equations, Review Exercises, and Practice Test
603(5)
Introduction to Statistics
608(37)
Frequency Distributions
609(4)
Measures of Central Tendency
613(4)
Standard Deviation
617(4)
Normal Distributions
621(6)
Statistical Process Control
627(5)
Linear Regression
632(5)
Nonlinear Regression
637(8)
Chapter Equations, Review Exercises, and Practice Test
641(4)
The Derivative
645(46)
Limits
646(8)
The Slope of a Tangent to a Curve
654(3)
The Derivative
657(4)
The Derivative as an Instantaneous Rate of Change
661(4)
Derivatives of Polynomials
665(5)
Derivatives of Products and Quotients of Functions
670(5)
The Derivative of a Power of a Function
675(6)
Differentiation of Implicit Functions
681(2)
Higher Derivatives
683(8)
Chapter Equations, Review Exercises, and Practice Test
687(4)
Applications of the Derivative
691(42)
Tangents and Normals
692(3)
Newton's Method for Solving Equations
695(3)
Curvilinear Motion
698(5)
Related Rates
703(4)
Using Derivatives in Curve Sketching
707(6)
More on Curve Sketching
713(5)
Applied Maximum and Minimum Problems
718(7)
Differentials and Linear Approximations
725(8)
Chapter Equations, Review Exercises, and Practice Test
729(4)
Integration
733(25)
Antiderivatives
734(2)
The Indefinite Integral
736(5)
The Area Under a Curve
741(5)
The Definite Integral
746(3)
Numerical Integration: The Trapezoidal Rule
749(3)
Simpson's Rule
752(6)
Chapter Equations, Review Exercises, and Practice Test
755(3)
Applications of Integration
758(39)
Applications of the Indefinite Integral
759(5)
Areas by Integration
764(6)
Volumes by Integration
770(5)
Centroids
775(7)
Moments of Inertia
782(5)
Other Applications
787(10)
Chapter Equations, Review Exercises, and Practice Test
792(5)
Differentiation of Transcendental Functions
797(34)
Derivatives of the Sine and Cosine Functions
798(5)
Derivatives of the Other Trigonometric Functions
803(3)
Derivatives of the Inverse Trigonometric Functions
806(4)
Applications
810(5)
Derivative of the Logarithmic Function
815(4)
Derivative of the Exponential Function
819(4)
Applications
823(8)
Chapter Equations, Review Exercises, and Practice Test
827(4)
Methods of Integration
831(44)
The General Power Formula
832(2)
The Basic Logarithmic Form
834(4)
The Exponential Form
838(3)
Basic Trigonometric Forms
841(4)
Other Trigonometric Forms
845(4)
Inverse Trigonometric Forms
849(4)
Integration by Parts
853(3)
Integration by Trigonometric Substitution
856(3)
Integration by Partial Fractions: Nonrepeated Linear Factors
859(4)
Integration by Partial Fractions: Other Cases
863(5)
Integration by Use of Tables
868(7)
Chapter Equations, Review Exercises, and Practice Test
871(4)
Expansion of Functions in Series
875(35)
Infinite Series
876(4)
Maclaurin Series
880(4)
Certain Operations with Series
884(4)
Computations by Use of Series Expansions
888(3)
Taylor Series
891(3)
Introduction to Fourier Series
894(7)
More about Fourier Series
901(9)
Chapter Equations, Review Exercises, and Practice Test
906(4)
Differential Equations
910(51)
Solutions of Differential Equations
911(2)
Separation of Variables
913(4)
Integrating Combinations
917(2)
The Linear Differential Equation of the First Order
919(3)
Elementary Applications
922(6)
Higher-Order Homogeneous Equations
928(4)
Auxiliary Equations with Repeated or Complex Roots
932(3)
Solutions of Nonhomogeneous Equations
935(5)
Applications of Higher-Order Equations
940(7)
Laplace Transforms
947(5)
Solving Differential Equations by Laplace Transforms
952(9)
Chapter Equations, Review Exercises, and Practice Test
956(5)
Supplementary Topics
961
Higher-Order Determinants
961(6)
Gaussian Elimination
967(3)
Rotation of Axes
970(4)
Functions of Two Variables
974(3)
Curves and Surfaces in Three Dimensions
977(6)
Partial Derivatives
983(4)
Double Integrals
987(4)
Numerical Solutions of Differential Equations
991
Appendix A Study Aids
1(3)
A.1 Introduction
1(1)
A.2 Suggestions for Study
2(1)
A.3 Solving Word Problems
3(1)
Appendix B Units of Measurement; The Metric System
4(6)
B.1 Introduction
4(3)
B.2 Reductions and Conversions
7(3)
Appendix C The Graphing Calculator
10(8)
C.1 Introduction
10(1)
C.2 The Graphing Calculator
10(4)
C.3 Graphing Calculator Programs
14(4)
Appendix D Newton's Method
18(1)
Appendix E Table of Integrals
19
Answers to Odd-Numbered Exercises 1(1)
Solutions to Practice Test Problems 1(1)
Index of Applications 1(10)
Index of Writing Exercises 11(2)
Index 13


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